We first note that for all angularities — groomed or ungroomed — the difference
between the derivatives of \(\Sigma _\text{LO}\)  and \(\Sigma _\text{exp LO}\) 
vanishes for \(\lambda \ll 1\) , as expected in the ungroomed case. For the groomed angularities
there are in principle, for \(\beta = 0\) , deviations of
\(\mathcal {O}(z_{\text{cut}})\) . Those appear to be too small to observe numerically here,
as was also observed for example for event shapes in [1]}. In comparing
\(d\Sigma _\text{NLO}/dL\)  and
\(d\Sigma _\text{exp NLO}/dL\)  (with \(L\equiv \log (1/\lambda )\) ) we
observe a linearly rising difference, indicating missing
terms of order \(\alpha _\text{s} ^2 L^2\)  in \(\Sigma _\text{exp NLO}\) . By including the
\(C^{\delta ,(1)}\)  coefficient in \(\Sigma _\text{exp NLO+C}\) , the derivatives
only differ by a constant, confirming that missing terms in the
cumulative distribution are reduced to order \(\alpha _\text{s} ^2 L\) .
